عنوان مقاله [English]
Rivers undergo many changes over time caused by various factors, such as geological, hydrological, and geomorphological features. One of the key topics in river engineering is the identification of river patterns (i.e. morphology). The study of the morphological aspects of rivers has always attracted the attention of specialists. Meandering rivers are among the most common types of rivers in nature with a linear form and very complex currents. The identification of these currents, which leads to the prediction of geometric pattern changes to rivers, requires sophisticated research tools. Fractal and multi-fractal analyses are among the most powerful analysis methods used in nonlinear systems to investigate complex patterns. This paper aims to investigate the Qara Aghaj River drainage basin in Fars province based on the multi-fractal geometry analysis of the waterway evolution process as well as the adaptive comparison derived from the regression operation of the multi-fractal parameters of the drainage basin with the central angle index of (A).
The Qara Aghaj River drainage basin is located on the eastern slopes of the Zagros Mountains between longitude of 47-51 and 14-54 N and latitude of 22-28 to 29-54 E. This drainage basin has an area of 13,050 km2. The drainage basin is bounded by the Kor River drainage basin as well as the Bakhtegan and Maharloo Lake drainage basin in the north, by the Kol River drainage basin in the east, by the Mand River drainage basin in the south, and by the Shapur and Dalaki River drainage basin in the west. In the fractal study of the Qara Aghaj River drainage basin in the Fars province, taking into account 3 study periods of the river, very high-quality satellite images were captured in those periods. ArcGIS software was used to perform image correction and process operations. After performing advanced image processing operations to extract the water pattern of the river in ArcGIS software, the river water pattern’s polygon file for all 3 study periods was transferred to AutoCAD software to measure the central angle morphology index (A). To determine the size of the central angle index, arcs were fit to each of the meanders with high precision in AutoCAD software for periods 1 to 3 of the river. Each of the meanders in the river is actually a river arc, with the successive river arcs being the focal point of this research for examining their evolution.
After checking the numerical value of each arc in the periods, given the numerical mean of the central angle of 115° for period 1 of the river, 108° for period 2, and 98° for period 3, which were all located within the numerical range of 85° and 158° (158> 115> 108> 98> 85), it was found out all the three selected river periods were of the developed meandering type. However, in the present study, the evolution pattern of the river was evaluated to examine the multi-fractal parameters. Accordingly, period 1 of the river included 22 evolution patterns, period 2 of the river included 23 evolution patterns, and period 3 of the river included 17 evolution patterns. According to the evolution trend of the calculated values, each morphological index of the central angle (A) for periods 1 to 3 of the river was calculated based on the average of its previous values, for each of the evolution patterns. In the present study, Fractalyse software was used to calculate each evolution pattern of periods 1 to 3 of the river. Upon importing the *.tiff image file of each evolution pattern for periods 1 to 3 of the river and using the box-counting method for calculating multi-fractal parameters, all analyzed numbers were exported in the form of *.txt files. Next, they were used for drawing diagrams and correcting some output errors of models in Microsoft Excel.
Results and Discussion
In the present study, given the study of the river evolution patterns for finding logical relationships between the central angle morphology index (A) and multi-fractal parameters, we deal with a lot of numbers in each pattern. Thus, the review of this subject was not possible without drawing a diagram, given the huge amount of data, all of which consisted of numbers and figures. Therefore, to examine more accurately and to convert all these numbers into a comparable criterion, multivariate regression analysis and the R2 regression coefficient were used for each diagram. To this end, for each of periods 1 to 3 of the river, the value of R2 was determined by drawing the diagram of the central angle in the order of the evolutionary pattern of successive arcs. Next, to create a certain weight ratio through multiplying the values of the central angles by each of the 15 corresponding multi-fractal parameters, the new value of R2 was determined.
The results obtained from running 180 regression diagram models in Excel software indicate that the evolution patterns of the river are affected by multi-fractal features. Parameters, such as 〖∆,D〗_f,〖Dq〗_((2) ),〖τq〗_((o) ),〖Dq〗_((max) ),〖Dq〗_((min) ), as well as α_((max) ), most of which being related to generalized and fractal dimensions, had the highest percentage of effectiveness in increasing the numerical value of the R2 regression coefficient in all periods 1 to 3 of the river. With a more detailed review, it was finally concluded that in the evolution pattern of period 1 of the river which had a more regular rhythm of successive arcs than the other two periods, i.e. periods 2 and 3, significant differences were produced in the results. This indicates that the central angles of the arcs in the river are always of great importance, and that they are very effective in the way the arcs are formed. In the end, we always witness how carefully the nature puts such angles and distances together, thereby creating a special order in the pattern of the complex mathematics of these natural phenomena.